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Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations. Check FAQs
Ishaft=4f2wLshaft4π2Eg
Ishaft - Moment of inertia of shaft?f - Frequency?w - Load per unit length?Lshaft - Length of Shaft?E - Young's Modulus?g - Acceleration due to Gravity?π - Archimedes' constant?

Moment of Inertia of Shaft given Natural Frequency Example

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With units
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Here is how the Moment of Inertia of Shaft given Natural Frequency equation looks like with Values.

Here is how the Moment of Inertia of Shaft given Natural Frequency equation looks like with Units.

Here is how the Moment of Inertia of Shaft given Natural Frequency equation looks like.

10053.5944Edit=490Edit23Edit3.5Edit43.1416215Edit9.8Edit
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Moment of Inertia of Shaft given Natural Frequency Solution

Follow our step by step solution on how to calculate Moment of Inertia of Shaft given Natural Frequency?

FIRST Step Consider the formula
Ishaft=4f2wLshaft4π2Eg
Next Step Substitute values of Variables
Ishaft=490Hz233.5m4π215N/m9.8m/s²
Next Step Substitute values of Constants
Ishaft=490Hz233.5m43.1416215N/m9.8m/s²
Next Step Prepare to Evaluate
Ishaft=490233.543.14162159.8
Next Step Evaluate
Ishaft=10053.594446911kg·m²
LAST Step Rounding Answer
Ishaft=10053.5944kg·m²

Moment of Inertia of Shaft given Natural Frequency Formula Elements

Variables
Constants
Moment of inertia of shaft
Moment of inertia of shaft is the measure of an object's resistance to changes in its rotation, influencing natural frequency of free transverse vibrations.
Symbol: Ishaft
Measurement: Moment of InertiaUnit: kg·m²
Note: Value should be greater than 0.
Frequency
Frequency is the number of oscillations or cycles per second of a system undergoing free transverse vibrations, characterizing its natural vibrational behavior.
Symbol: f
Measurement: FrequencyUnit: Hz
Note: Value can be positive or negative.
Load per unit length
Load per unit length is the force per unit length applied to a system, affecting its natural frequency of free transverse vibrations.
Symbol: w
Measurement: NAUnit: Unitless
Note: Value should be greater than 0.
Length of Shaft
Length of Shaft is the distance from the axis of rotation to the point of maximum vibration amplitude in a transversely vibrating shaft.
Symbol: Lshaft
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Young's Modulus
Young's Modulus is a measure of the stiffness of a solid material and is used to calculate the natural frequency of free transverse vibrations.
Symbol: E
Measurement: Stiffness ConstantUnit: N/m
Note: Value should be greater than 0.
Acceleration due to Gravity
Acceleration due to Gravity is the rate of change of velocity of an object under the influence of gravitational force, affecting natural frequency of free transverse vibrations.
Symbol: g
Measurement: AccelerationUnit: m/s²
Note: Value should be greater than 0.
Archimedes' constant
Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.
Symbol: π
Value: 3.14159265358979323846264338327950288

Other Formulas to find Moment of inertia of shaft

​Go Moment of Inertia of Shaft given Static Deflection given Load per Unit Length
Ishaft=5wLshaft4384Eδ
​Go Moment of Inertia of Shaft given Circular Frequency
Ishaft=ωn2w(Lshaft4)π4Eg

Other formulas in Uniformly Distributed Load Acting Over a Simply Supported Shaft category

​Go Circular Frequency given Static Deflection
ωn=2π0.5615δ
​Go Natural Frequency given Static Deflection
f=0.5615δ
​Go Uniformly Distributed Load Unit Length given Static Deflection
w=δ384EIshaft5Lshaft4
​Go Length of Shaft given Static Deflection
Lshaft=(δ384EIshaft5w)14

How to Evaluate Moment of Inertia of Shaft given Natural Frequency?

Moment of Inertia of Shaft given Natural Frequency evaluator uses Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity) to evaluate the Moment of inertia of shaft, Moment of Inertia of Shaft given Natural Frequency formula is defined as a measure of the shaft's resistance to changes in its rotation, which is essential in determining the natural frequency of free transverse vibrations in a shaft, providing valuable insights into the shaft's dynamic behavior and stability. Moment of inertia of shaft is denoted by Ishaft symbol.

How to evaluate Moment of Inertia of Shaft given Natural Frequency using this online evaluator? To use this online evaluator for Moment of Inertia of Shaft given Natural Frequency, enter Frequency (f), Load per unit length (w), Length of Shaft (Lshaft), Young's Modulus (E) & Acceleration due to Gravity (g) and hit the calculate button.

FAQs on Moment of Inertia of Shaft given Natural Frequency

What is the formula to find Moment of Inertia of Shaft given Natural Frequency?
The formula of Moment of Inertia of Shaft given Natural Frequency is expressed as Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity). Here is an example- 10053.59 = (4*90^2*3*3.5^4)/(pi^2*15*9.8).
How to calculate Moment of Inertia of Shaft given Natural Frequency?
With Frequency (f), Load per unit length (w), Length of Shaft (Lshaft), Young's Modulus (E) & Acceleration due to Gravity (g) we can find Moment of Inertia of Shaft given Natural Frequency using the formula - Moment of inertia of shaft = (4*Frequency^2*Load per unit length*Length of Shaft^4)/(pi^2*Young's Modulus*Acceleration due to Gravity). This formula also uses Archimedes' constant .
What are the other ways to Calculate Moment of inertia of shaft?
Here are the different ways to Calculate Moment of inertia of shaft-
  • Moment of inertia of shaft=(5*Load per unit length*Length of Shaft^4)/(384*Young's Modulus*Static Deflection)OpenImg
  • Moment of inertia of shaft=(Natural Circular Frequency^2*Load per unit length*(Length of Shaft^4))/(pi^4*Young's Modulus*Acceleration due to Gravity)OpenImg
Can the Moment of Inertia of Shaft given Natural Frequency be negative?
No, the Moment of Inertia of Shaft given Natural Frequency, measured in Moment of Inertia cannot be negative.
Which unit is used to measure Moment of Inertia of Shaft given Natural Frequency?
Moment of Inertia of Shaft given Natural Frequency is usually measured using the Kilogram Square Meter[kg·m²] for Moment of Inertia. Kilogram Square Centimeter[kg·m²], Kilogram Square Millimeter[kg·m²], Gram Square Centimeter[kg·m²] are the few other units in which Moment of Inertia of Shaft given Natural Frequency can be measured.
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